Igusa–Liu–Paquette extension conjecture

Let $S$ be a simple module over an artin algebra. Igusa–Liu–Paquette extension conjecture. If

$$\operatorname{Ext}^1(S,S)\neq 0,$$

then

$$\operatorname{Ext}^i(S,S)\neq 0$$

for infinitely many integers $i$. This is presented as a stronger statement related to the Strong No Loop Conjecture; the source attributes it to K. Igusa, S. Liu, and C. Paquette and does not state that it has been resolved.